Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell.

Necessary condition indicator: only if

Components: Students are cited as "late" AND only if they arrive 5+ mins past the last homeroom bell ring

Translation: CAL and 5+

Lawgic: CAL --> 5+

Kumar arrived 17 minutes after the last ring of the homeroom bell.

Kumar being cited would NOT be a valid conclusion, because "only if" gives us a necessary condition. It tells us that arriving 5+ mins late is a necessary condition for being cited as late, but it does not mean that arriving 5+ mins late is sufficient to guarantee a citation. If a student is cited as late, they must have arrived 5+ mins late. But arriving 5+ mins late by itself does not guarantee that the student will be cited.

All we know is that Kumar satisfied the necessary condition, but the conditional statement tells us that this is not sufficient enough to validate that he will be cited. My question: What if we said, "He could be cited as late." Does this work? Does this follow logically? I finished this lesson a few hours ago and am still stuck on this....sorry if I am overanalyzing.

This is an example from the loophole: If Alex is breathing, then air is present. Alex is breathing.

Necessary condition indicator: then

components: Alex breathing AND air present

Translation: AB and AP

Lawgic: AB --> AP

If we were only given a statement, like "Alex woke up and air was present," that would not mean that Alex is necessarily breathing. All we know from the conditional statement, is that in order for Alex to be breathing, air MUST be present.

I appreciate the explanation for question 2. Specifically adding an additional step at the beginning where you reframe the sentence, so the sufficient comes first.

Question 2:

Amar would not want to learn to ski if he were over 40.

Reframe: If he were over 40, Amar would not want to learn to ski.

Question 1:

I would not be able to see Arun if he were in the next room.

Reframe: If he were in the next room, I would not be able to see Arun.

As I learn these concepts for the first time, I find this makes it a lot easier to move on with the rest of the translation.

To clarify, is question 4 a negative comparison? There is no statistical evidence to show that A happens more often than B, suggesting that there is no "clear" winner. If we were provided more context, we would then have to infer whether humans act selfishly more often than unselfishly? Or, am I to disregard "No statistical evidence is provided to show..." because the "kernel" of the comparison is in the latter part of the sentence? Sorry if this is a silly question

Same here. Currently reading the Odyssey and really enjoying it. I'm slowly becoming less intimated by complex, wordy sentences

"The Elizabethan era" is a modifier. The sentence still works as just "William Shakespeare (subject) captured (predicate-verb) the spirt (predicate-object)"

"The Elizabethan era" is additional information or details that help to situate the reader within the period in which William Shakespeare would've captured the spirt, but it is not necessary to the "kernel" of the sentence.

Thank you for this detailed breakdown! My initial thought was that the opening statement: "One method of dating the emergence of species is to compare the genetic material of related species" was the conclusion, because the information that follows supports this.

Upon completing the studies on the seven bear species, "scientists concluded that bears and raccoons diverged 30 to 50 million years ago. They further concluded that red pandas separated from the ancestor of today's raccoons and coatis a few million years later, some 10 million years before giant pandas diverged from the other bears." Wouldn't this information, that the scientists successfully dated the emergence of species by comparing the genetic material of the seven bear species (which are "related species") support the claim that one method of dating the emergence of species is to compare the genetic material of related species?